2. Verify that the Mean Value Theorem (MVT) applies to the function f(r) on the interval 37 and find all the values satisfying the conclusion of MVT.

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A: the solution is as follow we will solve the given problem by numerical method  Trapezoidal rule

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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Q: 2- consider the set of all finite subsets of N, is this set countable or not, prove it?

A: Consider the set of all finite subsets of N, is this set countable or not, to prove it.